The field of the disclosure relates generally to optical communication systems and networks, and more particularly, to faster-than-Nyquist modulation for optical systems and networks.
Conventional hybrid fiber-coaxial (HFC) architectures deploy long fiber strands from an optical hub to a fiber node, and typically many short fiber strands to cover the shorter distances from the HFC nodes to a plurality of end users. Conventional Multiple Service Operators (MSOs) offer a variety of services, including analog/digital TV, video on demand (VoD), telephony, and high speed data internet, over these HFC networks, which utilize both optical fibers and coaxial cables, and which provide video, voice, and data services to the end user subscribers. The HFC network typically includes a master headend, and the long optical fiber carries the optical signals and connects the link between the headend, the hub, and the fiber node. Conventional HFC networks also typically include a plurality of coaxial cables to connect the fiber nodes to the respective end users, and which also carry radio frequency (RF) modulated analog electrical signals.
The HFC fiber node converts optical analog signals from the optical fiber into the RF modulated electrical signals that are transported by the coaxial cables to the end users/subscribers. Some HFC networks implement a fiber deep architecture, and may further utilize electrical amplifiers disposed along the coaxial cables to amplify the RF analog signals. In the conventional HFC network, both the optical and electrical signals are in the analog form, from the hub all the way to the end user subscriber's home. Typically, a modem termination system (MTS) is located at either the headend or the hub, and provides complementary functionality to a modem of the respective end user.
The continuous growth of optical intra/inter-data-center link, 5G mobile fronthaul and backhaul, next-generation distributed HFC architectures and access networks, passive optical networks (PONs), and high-speed optical short-reach transmission systems with advanced multi-level modulation formats require an equivalent growth in the development of advanced digital multi-level modulation formats to process the vastly increased amount of data transmitted over the various networks. Presently, conventional deployments of 1G/10G PON systems using nonreturn to zero (NRZ) modulation are unable to meet the growing capacity demand to deliver future high-speed data and video services.
Pulse-amplitude-modulation (PAM) with four levels (PAM-4), using either eight or four wavelengths with 50 or 100 Gbps per lane, has been recently considered as one solution in the baseline of IEEE P802.3bs 200G/400G Ethernet standard. Optical four-level PAM-4 and eight-level PAM-8 modulation schemes have also been recently proposed for 100G and 400G long-haul transmission networks and intra/inter-datacenter connects. However, these proposed PAM implementations will introduce several technical challenges. For example, it is difficult to discontinuously upgrade existing systems from PAM-2K to PAM-2K+1, due to existing bandwidth and receiver sensitivity limitations. In another example, in back-to-back (B2B) transmission, changing from NRZ to PAM-4 will result in an approximately 4-dB system margin degradation, and similar when changing from PAM-4 to PAM-8. Additionally, other factors, such as chromatic dispersion and increased peak-to-average-power ratio (PAPR), may further degrade the transmission.
The requirements of conventional optical network system are presently unable to accommodate the jump from one modulation format to another, and both NRZ-based and PAM-based systems presently lack the flexibility to fully utilize the system capacity. A significant performance gap exists that greatly increases the complexity between different PAM formats, rendering a switch from one PAM format to another even further challenging and expensive. Thus, simply increasing the order of modulation has not proven to be a power-efficient and sustainable solution.
Other proposals for cost efficiency and low power consumption consider employment of existing 10-GHz or 20-GHz-bandwidth components. However, this proposal creates the separate challenge presented by the severe inter-symbol interference (IR) that occurs due to bandwidth constraints by operation at higher baud rates. Linear pre-equalization (PE) has been proposed to mitigate such impairments, but PE is not optimal because of the resulting sacrifice to the system dynamic range and overall signal performance. Furthermore, the experienced equalizer effect is worsened by the presence of non-white Gaussian noise at the bandwidth-limited receiver with matched filtering detection.
Instead of increasing the modulation levels, other technical proposals increase the transmitted symbol rate to be faster than the channel Nyquist limit, which is also referred to as faster-than-Nyquist (FTN) signaling. Conventional FTN techniques are limited by the complex processing necessary to deal with the cumbersome ISI that occurs. Some conventional equalizers and coding techniques address more severe cases ISI, so that the benefit from the increase in the data rate (i.e., beyond Nyquist) outweighs the potential information loss incurred by FTN-induced ISI. Some techniques increase the symbol clock frequency rather than discontinuously multiplying the discrete amplitude levels, to performance gap and more fully utilize the system margin with high scalability.
Some conventional FTN systems, under the influence of narrow-filtering (NF) effect, are modeled with a symbol rate significantly faster than its root-mean-square (RMS) bandwidth, and different digital-signal-processing (DSP) techniques have been proposed in these conventional FTN systems. Maximum-likelihood-sequence estimation (MLSE) and Bahl Cocke Jelineck Raviv (BCJR) decoders have been used to estimate channel memory states among multiple neighboring symbols.
MLSE-based techniques (e.g., including poly-binary shaped FTN systems) use an algorithm to counter FTN system ISI impairments. The algorithm considers multiple neighboring symbols to calculate the Euclidean distance and soft MLSE decision through Trellis searching, in order to improve the performance of the forward error correction (FEC). However, these techniques have been limited due to the phenomenon of adaptive-filter-convergence failures observed in experimental systems (e.g., FTN-DP-16 QAM), in part caused by the insufficient memory length under severe ISI. Furthermore, when ISI coefficients from more than two adjacent symbols are involved, the complexity of the corresponding Trellis table will also increase significantly, rendering the technique very difficult to implement in real systems, which is really hard to implement in the real systems.
BCJR-based techniques utilize an algorithm for an FTN receiver based on a Viterbi equalizer. The algorithm estimates the channel memory states and calculates the log likelihood ratio (LLR) of the information bits. However, such BCJR-based systems rely solely on post processing, and therefore experience significantly high computational complexity at the receiver. Similar to MLSE-based techniques, the complexity of BCJR will also significantly increase with a large channel memory depth. Tomlinson-Harashima precoding (THP)-based FTN scheme schemes use an algorithm that allows the system to trade-off the increased ISI into symbol constellation expansion, which eliminate the complex maximal likelihood search operation as in MLSE and BCJR. However, the resulting PAPR of the system using THP is increased, while power efficiency is decreased. Additionally, according to these THP techniques, training symbols lose their deterministic location on the constellation, which causes training-based adaptive algorithms to fail.
Therefore, as ISI increases, the complexity and memory requirements of Trellis searching and other FTN techniques expand significantly, thereby significantly increasing the cost and power consumption of the system. Additionally, all of these conventional FTN techniques are based on fixed-symbol-rate architectures which do not fundamentally differentiate the systems in which they are employed from different conventional fixed-rate multilevel modulated systems. Accordingly, it is desirable to create FTN systems and methods that are more economically feasible for existing and developing optical networks, and which consume power more efficiently.